Image filtering in structured illumination microscopy using the Lukosz bound

Abstract

Various aspects of image filtering affect the final image quality in Structured Illumination Microscopy, in particular the regularization parameter and type of regularization function, the relative height of the side bands, and the shape of the apodization function. We propose an apodization filter without adjustable parameters based on the application of the Lukosz bound in order to guarantee a non-negative point spread function. Simulations of digital resolution charts and experimental data of chromatin structures and of actin filaments show artefact free reconstructions for a wide range of filter parameters. In general, a trade-off is observed between sharpness and noise suppression.

XL-SIM: Extending Superresolution into Deeper Layers

“…Finally the frequency values of all bands are superimposed, according to Equation (2), which is a generalized Wiener filter [20,21,28,29]:…”

“…The parameter is the Wiener parameter, which has been chosen empirically andÃ( k) is an apodization function [21,29].…”

Three-dimensional structured illumination microscopy using Lukosz bound apodization reduces pixel negativity at no resolution cost

“…Note that these conditions are necessary but not sufficient. Previously we discussed how this set of rules can be used to derive the Lukosz-bound for 2D SIM in order to get a non-negative SIM PSF [19]. The 1D bound is given by connecting the tips of Lukosz' "stair case": where q c is the cut-off frequency.…”

“…This practice leads to unreliable final images for laymen users, and ultimately to biased biological results. Recently we described a method for SIM reconstruction in 2D [19] with the aim to reduce the number of free parameters and to ensure a non-negative Point Spread Function (PSF) by using the upper bound to the Modulation Transfer Function (MTF) as derived by Lukosz [20,21] as apodization function.…”

“…In section 2 we will shortly summarize the main reconstruction steps of [19], derive the parametrization of the 3D SIM cut-off, give an extension of the Lukosz bound to 3D, and compare 3D Lukosz bound and triangular apodization. Experimental validation will be presented in section 3, were the methods developed throughout the paper will be applied to images of actin filaments and DAPI-stained DNA structure in a cell.…”